5th International Conference on Civil Engineering and Transportation (ICCET 2015) Maintenance Scheduling Optimization for 30kt Heavy Haul Combined Train in Daqin Railway Yuan Lin1, a, Leishan Zhou1, b and Jinjin Tang1, c * 1School of Traffic and Transportation, Beijing Jiaotong University No.3 Shang Yuan Cun, Hai Dian District, Beijing, China.100044 [email protected], [email protected], [email protected] Keywords: railway transportation; maintenance scheduling; modeling and algorithm; Daqin Railway; 30kt heavy haul combined train Abstract. The freight demand on Daqin Railway is growing yearly, but the maintenance scheduling is almost based on field experience, which makes great impact on transport capacity. Based on maintaining theory, this paper focuses on modeling and algorithm, offering scientific maintenance scheduling for Daqin Railway. With the investigated data, it analyzes the current maintenance scheduling of Daqin Railway. Then the paper models maintenance scheduling based on description of an example illustration, aiming at the least impact of maintenance scheduling on train scheduling. With the algorithm ready, the train operation database is established and the scheduling solving system is developed. Finally, a theoretical maintenance scheduling is provided for 30kt heavy haul combined train in Daqin Railway. The offered maintenance scheduling can meet the actual demand with different maintaining durations. Introduction Daqin Railway is known as the important passageway for western coal transportation and the first double-track electrified heavy haul railway in China. It’s 653km long, stretching from Datong in the west to Qinhuangdao in the east. The freight volume of Daqin Railway is keeping in a steady increasing from 103 million tons in 2002 to 450 million tons in 2014 [1], and it’s predicted to reach 460 million tons in 2015. To meet the growing demand of freight transport, the trial of 30kt heavy haul combined train which consists of 5 locomotives and 315 wagons, totally weight 31.5kt, has been carried out successfully on April 2nd, 2014 [2]. As an important part of train scheduling, maintenance scheduling must be scientific and reasonable, which may greatly contribute to improve the transport capacity of Daqin Railway. Many scholars [3]-[5] have studied on maintenance scheduling in different aspects just with qualitative analysis. Zhen Li [6] quantitatively models the time as well as duration of maintenance scheduling and then designs the algorithm to optimize them, but the line researched is quite simple and the solution is only calculated by manual. Lei Nie [7] models Rectangle-maintenance scheduling to obtain the optimal maintaining time aiming at the minimum of train affected by maintenance scheduling, which has certain reference significance to the heavy-haul railway transportation. Analysis of Current Maintenance Scheduling Currently, Daqin Railway adopts centralized maintenance as well as routine maintenance. Centralized maintenance is adopted continuously during 9:00-12:00 about forty times in spring and autumn yearly. Routine maintenance is adopted once every ten-day during 10:00-12:00 in summer and autumn, while 04:20-06:20 or 5:00-7:00 in winter and spring. Besides, maintenance scheduling are classified into V-maintenance and Rectangle-maintenance according to maintaining type. If we adopt the V-maintenance in electrified railway, the operating track will charge up the maintaining track, leaving great safety risks in operation. So the types of centralized and routine maintenance in Daqin Railway are almost Rectangle-maintenance, which forbids trains to operate on both tracks during maintaining. © 2015. The authors - Published by Atlantis Press 440 With the data about daily transportation from 2012 to 2014, here makes statistical analysis on average amount of daily loaded trains delivered from Hudong marshalling station in centralized maintenance day, routine maintenance day and regular day in Table 1. Amount of trains in Amount of trains in Amount of trains in Year centralized maintenance routine maintenance regular day day day 2012 72 77 87 2013 72 79 90 2014 71 78 88 Table 1. Averages of loaded trains delivered in different situations from 2012 to 2014 In 2013, it’s shown that the amount of daily loaded trains delivered in centralized maintenance day is 17 less than that in regular day, while the amount in routine maintenance day is 11 less than that in regular day. So the current maintenance scheduling has a great impact on train operation. The maintaining type in Daqin Railway is almost Rectangle-maintenance, which is of science foundation because of the limit of electrified railway’s characteristics. But maintaining time and maintaining duration are only based on field experience without available theory support. What’s worse, there is no evaluation mechanism for implementation benefits of the maintenance scheduling. In the near future, Daqin Railway is about to operate the 30kt heavy haul combined train, which sets higher requirement for train scheduling as well as maintenance scheduling. Actually, the current maintenance scheduling should make a great adjustment to adapt to the new requirements. And it’s hoped that Daqin Railway can enlarge transport capacity to meet the rising freight demand. Therefore, we must adopt scientific maintenance scheduling, providing powerful guarantee for growth of freight volume. Connected with practice, this paper will model maintenance scheduling based on theory, providing a scientific maintenance scheduling for Daqin Railway. Modeling Maintenance Scheduling Example Illustration. As Fig. 1(a) shows, line MN is a simple railway network with five stations: M, A, B, C, N, and section MA, AB, BC, CN are maintaining sections divided by power supply sections. Fig. 1(b) is timetable of line MN, where we assume section AB adopts a Rectangle-maintenance about one hour at 19:00. The shaded rectangle represents the occupation period and space of maintenance. The trains affected during maintaining are L1, L2, and L3 in down direction and L4 in up direction. 441 (a) A simple railway network 18:00 19:00 20:00 21:00 M j+t - tki Tki - tki A L5 L1 L4 L3 B L2 L6 Tki - tki Tki - j C N 18:00 19:00 20:00 21:00 (b) Train timetable of the railway network Fig. 1. A simple railway network and its train timetable Parameters Description. Firstly, make explanation to the section and the time. 1) Section: Number the maintaining sections starting from 1 in down direction. For example, MA, AB, BC, CN section is numbered as 1, 2, 3 and 4 in order. The section is symbolized by k . 2) Time: Set 18:00 as number 0 hour and measure the time in minute. It’s not to zero if the time is more than 24h (1440min). For example, 20:00 is 120min, and 19:00 in next day is 1500min. Then, some related parameters are described as follow: I : Total amount of trains in train timetable. i : Ordinal number of train in train timetable. K : Total amount of maintaining sections. k : Ordinal number of maintaining section start from 1. J : Departure hour of the latest train. j : Possible time of starting maintenance and ordinal number of hour starting from 0. T : Maximum maintaining duration. t : Maintaining duration. tki : Departure time of train i at the former station of section k . Tki : Arrival time of train i at the latter station of section k . fk t j i : Impact coefficient, representing the impact extent on train i when maintenance scheduling is adopted during []j,j+t in section k . fk t j : Total impact coefficient, representing the impact extent on train scheduling when maintenance scheduling is adopted during []j,j+t in section k . According to parameters description, if the maintenance scheduling is adopted during []j,j+t in number k section, the impact coefficient fk t j i of train k , is equal to the ratio of []tk i,Tk i within[]j,j+t . 442 [tki,Tki ]I[]j,j+t e.g. f=k t j i (1) [tTki,]ki If there are I trains in train timetable, the total impact coefficient is calculated as I fk t j =få k t j i (2) i=1 Constraints and Objective Function. According to the power supply sections, the line is divided into 22 maintaining sections. So all the researching sections are k Î {1,2,3，...10,...,21,22} (3) Now, the maintenance for Daqin Railway are almost Rectangle-maintenance. To ensure maintaining efficiency, the minimum duration is 2h because of subsidiary time for the large machine. In addition, large mechanical efficiency in 5 hours’ maintenance is higher than 4 hours’ maintenance [6]. In the future, Daqin Railway may elongate maintaining duration to improve its efficiency. Therefore, the maximum duration, T, is determined as 5h. So the constraint of duration is t Î {2,3,4,5} (4) Maintenance scheduling need to take period, stuff shifts and repast into account. Because of the complex situation, the paper doesn’t restrict the maintaining time, only to fetch the optimal maintaining time for each section in theory. So the constraint of time is j Î {0,1,2，...11,...,22,23} (5) If the section and the duration are determined, we can figure out fk t j of maintenance scheduling adopted in each time and fetch min fk t j . With analysis above, the model of maintenance scheduling for or 30kt heavy haul combined train in Daqin Railway can be formulated as ì (Tki-j) (Tki-tki) tki<j<Tki <j+t ï II ï1 j££tki<Tki j+t min f=min f=min k t j ååk t j i í i=11i= ï( j+t-tki)(Tki-tki ) j<tki<j+t<Tki ï îï0 j>Tkiorj+t<tki ì k Î {1,2,3,...,22} ï s.t.tí Î {}2,3,4,5 ï îï jÎ {0,1,2,...,23} (6) Model Solution Algorithm.